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درس کنترل ديجيتال مهر 1391 PowerPoint PPT Presentation


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بسم ا... الرحمن الرحيم. درس کنترل ديجيتال مهر 1391. دکتر حسين بلندي/دکتر سید مجید اسماعیل زاده/ دکتر بهمن قربانی واقعی. Discretization of Continuous-Time State Space.

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درس کنترل ديجيتال مهر 1391

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Discretization of Continuous-Time State Space

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fixed .


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Identity .


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T=1

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Anonsingular Asingular . (1) (2) .


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4) 2 N.S.D P . 2 .


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P.D N.D .

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Remarks


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2)

a .

ATP+PA=-I


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a<0 .


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  • . V(x)v(x(k))=V(x(k+1)T)-V(x(kT)) .

  • x(k+1)=Gx(k) x n Q nonsingular n*n x=0 .

  • V(x(k))=x*(k)Px(k) .P .


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v(x(k))=V(x(k+1))-V(x(k))

=x*(k+1) P x(k+1)-x*(k) P x(k)

=[Gx(k)]* P [Gx(k)]-x*(k) P x(k)

=x*(k) G* P G x(k)-x*(k) P x(k)

=x*(k)[G*PG-P]x(k)

v(x(k)) V(x(k))=-x*(k)Qx(k) -Q=[G*PG-P] . Q .


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Q P :

G*PG-P=-Q

P .


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x(k+1)=Gx(k) .

X n

G nonsingular , n*n

0=x Q P ( ) :

G*PG-P=-Q

x*Px V(x(k))=-x*(k)Qx(k) Q .


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:

P v(x(k))=-xTQx .


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. .


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k >1 .


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k .


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k1 k2 . 2 . .


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y(t) x(t) .


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